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A Hierarchy of Hyperbolic Models Linking Boltzmann to Navier Stokes Equations for Polyatomic Gases
Author(s) -
Le Tallec P.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200011)80:11/12<779::aid-zamm779>3.0.co;2-i
Subject(s) - ansatz , boltzmann equation , navier–stokes equations , mathematics , statistical physics , moment (physics) , boltzmann constant , distribution function , mathematical analysis , non dimensionalization and scaling of the navier–stokes equations , classical mechanics , physics , mathematical physics , compressibility , mechanics , thermodynamics
The paper describes and extends to polyatomic gases a general strategy for building a hierarchy of numerical models relating the Boltzmann and the Navier‐Stokes equations. It is based on two recent mathematically consistent ansatz, namely gaussian BGK collision models and Levermore's moment expansions, and preserves entropy, hyperbolicity, and relaxation constants. We can then adapt the general adaptive algorithm previously developed for coupling Navier‐Stokes equations to local kinetic models. In this process, the Navier‐Stokes equations are obtained by a Hilbert asymptotic expansion of the moment's equations, which gives them a kinetic interpretation in terms of a positive distribution function associated to the fifteen moments used in Levermore's expansion.